There have been a few that have been mentioned already that I would definitely put on that list:
"Bohemian Rhapsody" by Queen might be damn near the top of that list for just because of how amazingly constructed and off the wall it is. Like, seriously, its this super operatic tune that tells this pretty haunting story, and when it builds up into that fucking awesome riff before Freddie belts "SOO YOU THINK YOU CAN STOP ME AND SPIT IN MYY EEEYYYYYEEE!" How can you not just get pumped?! Legitimately, I would love to see more bands take that kind of approach to song writing and create something as all over the place while still remaining dynamic and coherent in its structure.
"Stairway to Heaven" by Led Zeppelin, I feel like saying anything about this song would just be redundant at this point, but at the same time just saying "its fucking awesome" doesn't really give justice to the kind of piece of art this song is. Its a perfect example of a song that just builds as it goes, just adding and adding until it hits a very literal climax. The lyrics are poetic, on point, and delivered with an inflection that just nails their lamenting nature, and that solo, that FUCKING solo from Jimmy Paige. I know these guys were accused of stealing a lot, and this song was the subject of a recent lawsuit (though I've listened to both and I don't buy it), but honestly, this is one of the few cases where if it was stolen, they improved upon it so much that it transcends whatever original subject matter it took from.
Two I was surprised were not mentioned yet was "Hurt" by Johnny Cash, and yeah, I know its a cover, and the original is a pretty darkly beautiful piece from NIN, but something about the way Johnny Cash does it (even excluding the knowledge he died shortly after) just makes it fucking heart wrenching, even to the point where the clipping towards the end of song (not sure if intentional or another example of Rick Rubin over compressing the song) actually adds to it in this sort of Too-Passionate-To-Be-Contained way. Its a fairly simple song, nothing overly complex musically speaking, but thats really its strength, its just powerful song writing.
Second one is "American Pie" by Don McLean which is amazing for its vivid lyricism painting a very effective portrait of an entire generation with one of the most memorable choruses in all of musicdom. The energy and musicality of this song is totally immersive and every time it plays I just get totally into it.
Some I would personally add that I think should get more intention (but I'll spare you all me gushing over them [AS MUCH] because I'm not that sadistic) include (links to each included):
"Big Bird" by AJJ (Formerly known as Andrew Jackson Jihad), what I will say, not sure if it works as well if you aren't familiar with the band, but this song is fucking sad, like an anxiety anthem of sorts.
"Machete" by Amanda Palmer I know there are a lot of people out there who, for some reason I don't understand, hate her, but Amanda Palmer is literally one of my heroes, and MAN was it fucking hard to pick a song of hers haha.
"Lost" By Amanda Palmer and the Grand Theft Orchestra SO HARD IN FACT, that I categorized her and this band as two separate projects so I could pick another song of hers (not that there was any rules about posting two songs from the same band/musician [Also, was STILL really hard to pick one from this album]).
"Turn Those Clapping Hands Into Angry Balled Fist" by Against Me! Fucking bitterness, cynicism, building instrumentation, and fucking energy! The climax of this song goes so hard, and I wish more punk bands would take a few pages at least from this band's work from around this era.
"I'm Serious, I'm Sorry" by Jeff Rosenstock This was another where it was hard to pick one song. Jeff is an AMAZING song writing, and the album "We Cool?" is filled, front to back with dynamic song structure, great musicianship, and deep and honest lyricism. This song exemplifies Jeff's attention to detail in music and song building. I'mma gonna have to listen to this album again.
I picked a lot of these songs, because I feel like they show a sense in modern music where great musical ideas meet good writing and structure, because there are a lot of examples of times when there are great musical ideas, great production ideas, great lyrics, but they never seem to meet, so to see songs where it all comes together to make an incredibly immersive experience is something I think is important to highlight in a world where people are constantly shitting on modern music and saying there are "no more good bands/musicians/songs etc. etc. etc."
I know there are A LOT of songs that might go unmentioned in this thread, it is a difficult question, but its nice to have a thread where the main objective isn't to just out name drop someone, but to actually discuss what in a song is so memorable to a point where it has staying power or comes off as almost timeless.